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1
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It's not the same type of problem over and over. You guys are going to have to use your thinking skills, your inductive reasoning to determine, hey, which property am I going to want to use?
2
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Because like I said over here, look over here. This one's difficult. This one says e raised to that. So if you're going to use that same latch with thinking, I have to put e, you'd have to, you know, I would represent negative 2 as e raised to some number.
3
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Well, that's can't work because e is, you know, a, is an international number. However, I can use my other one to one property and my other actually there's two different ways to do this. One way, it's positive, it's positive.
4
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Okay, first way I can do this is I can go back to last section. Remember when we first learned logarithmic or logs, we learned how to go from log form to exponential form. That's how explained what a logarithm was. Logrhythm is just really an exponent. It's just a way to represent an exponent.
5
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So one way I can see this, I say, one minute is right this has a lot. So I'm going to have l n, I already know it's base e because you remember your base throw the same l n of 2 equals x.
6
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Okay, so that's one way to solve it. The other way you can solve it is you can say, well, if I have e to the x equals 2, it is possible for me to take the logarithm, the natural logarithm of both sides.
7
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Remember, just like an equation, if I, you can add a one, remember like a regular equation you have 2 plus x equals 4. Now it's just, I need to use that. 6. You guys subtract that whole size, right?
8
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You're allowed, whatever you do, you just have to make sure you do it on both sides. So you can take the log of both sides. Now you'd say, why the heck would you ever want to do that?
9
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I understand why you're taking the negative 2, that's easy. You need to solve Rex. Here, why would I take the logarithm of both sides? Well, the reason why I took the natural logarithm of both sides is because, remember, my inverse properties?
10
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Now, I'm left with l n of e, which I know l n of e, right? This is a little base e, e raised to what never needs to e.
11
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It's one, right? And whenever you have an f, your base and your logarithm are raised to the same number, that's just going to cancel out and it's just going to leave you an x. That's your inverse property that I did previously.
12
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So there are 4 x equals l n of 2. So, like I was telling you, there's two different ways to do it.
13
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The third way it kind of really makes sense to you. You do need to understand this method because not always, you know, you're going to have more difficult problems that understand this method is going to be powerful of taking the log of both sides. The natural logarithm of both sides.
14
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Okay, that was number 19, and you guys want 21?